General Physics with Calculus I

Course Description

PHY2048 / PHY2048C – General Physics with Calculus I is a 4-credit lecture course (5 credits when including the integrated laboratory) in the Physics taxonomy of Florida's Statewide Course Numbering System (SCNS). The course is the calculus-based introductory physics course required for engineering, physics, mathematics, computer science, and related STEM majors. Students apply calculus to develop a quantitative understanding of classical mechanics, including kinematics, Newton's laws of motion, work and energy, momentum and collisions, rotational motion and angular momentum, gravitation, oscillations, fluid mechanics, and waves.

PHY2048 is part of Florida's state-mandated General Education Core in Natural Sciences (Physical Sciences), satisfying the Gen-Ed natural-science requirement at every Florida public college and university. The course is offered at 44 Florida public institutions and transfers as equivalent across the state. The "C" suffix variant denotes integrated lecture and laboratory components; the lecture-only form (PHY2048) is typically paired with the separate laboratory PHY2048L / PHYL2048. Together with PHY2049 (General Physics with Calculus II), this forms the standard two-course calculus-based physics sequence required for engineering and physics majors.

Learning Outcomes

Required Outcomes

Upon successful completion of this course, students will be able to:

• Apply calculus operations to kinematics: compute position, velocity, and acceleration as derivatives and integrals of position functions; solve problems involving constant and variable acceleration in one and two dimensions, including projectile motion.
• Apply Newton's laws of motion to analyze forces and motion, including problems involving friction, tension, normal forces, and connected systems.
• Apply work-energy theorem and conservation of mechanical energy to solve problems involving kinetic energy, potential energy (gravitational, elastic), and non-conservative forces.
• Apply conservation of linear momentum and impulse to solve problems involving collisions (elastic and inelastic) and explosions.
• Apply circular motion and rotational kinematics/dynamics, including angular displacement, angular velocity, angular acceleration, torque, moment of inertia, and rotational kinetic energy.
• Apply conservation of angular momentum to rotational systems.
• Apply Newton's law of universal gravitation to planetary motion and satellite orbits; understand Kepler's laws.
• Analyze simple harmonic motion (SHM), including spring-mass systems and pendulums; relate SHM to circular motion.
• Apply principles of fluid statics and fluid dynamics, including pressure, buoyancy (Archimedes' principle), and Bernoulli's equation.
• Analyze mechanical waves, including wave properties (frequency, wavelength, speed), superposition, and standing waves.
• Use algebra, trigonometry, vectors, and calculus to formulate and solve quantitative physics problems; identify relevant physical principles in given problems.
• Identify and analyze relevant information presented in various formats, including graphs, tables, diagrams, and mathematical formulations.
• Apply critical thinking and problem-solving to real-world physics problems and assess experimental results.

Optional Outcomes

Depending on institutional emphasis, students may also:

• Conduct laboratory experiments investigating mechanics, including data collection with motion sensors, force probes, and computer-based instrumentation; perform error analysis and report writing (when paired with PHY2048L or in PHY2048C).
• Apply thermodynamics fundamentals, including temperature, heat, the first law of thermodynamics, and the kinetic theory of gases.
• Solve more complex two-dimensional dynamics problems, including non-inertial reference frames.
• Use computational methods (Python, MATLAB, Mathematica, spreadsheets) to model physical systems and verify analytical results.
• Analyze damped and forced oscillations, including resonance.

Major Topics

Required Topics

• Measurement and Vectors: Units (SI), dimensional analysis; significant figures; vector addition, subtraction, components; dot and cross products of vectors.
• Kinematics in One Dimension: Position, displacement, velocity, acceleration; constant acceleration kinematic equations; free fall; calculus-based kinematics (velocity as derivative of position, acceleration as derivative of velocity).
• Kinematics in Two Dimensions: Position, velocity, and acceleration as vectors; projectile motion; uniform circular motion (centripetal acceleration); relative motion.
• Newton's Laws of Motion: First law (inertia); second law (F = ma); third law (action-reaction); free-body diagrams; common forces (gravity, normal force, friction, tension); applications to inclined planes, pulleys, connected systems.
• Friction and Drag: Static and kinetic friction; coefficient of friction; air resistance and terminal velocity (introductory).
• Circular Motion and Newton's Laws: Centripetal force; banked curves; vertical circles; non-uniform circular motion.
• Work, Energy, and Power: Work done by constant and variable forces (using line integrals); kinetic energy and the work-energy theorem; conservative and non-conservative forces; potential energy (gravitational, elastic); conservation of mechanical energy; power.
• Linear Momentum and Collisions: Linear momentum and impulse; conservation of linear momentum; one- and two-dimensional collisions (elastic, inelastic, perfectly inelastic); center of mass.
• Rotational Motion: Angular kinematics; rotational dynamics; torque; moment of inertia (calculation by integration); rotational kinetic energy; rolling motion; angular momentum and conservation.
• Static Equilibrium: Conditions for static equilibrium; analysis of beams, ladders, and other extended objects in equilibrium.
• Gravitation: Newton's law of universal gravitation; gravitational potential energy; Kepler's laws; orbital motion; escape velocity.
• Oscillations: Simple harmonic motion (SHM); spring-mass system; pendulum (simple, physical); energy in SHM; relationship between SHM and uniform circular motion.
• Fluid Mechanics: Density and pressure; pressure variation with depth; Archimedes' principle and buoyancy; ideal fluid flow; continuity equation; Bernoulli's equation.
• Mechanical Waves: Properties of waves (wavelength, frequency, period, speed); transverse and longitudinal waves; wave equation; superposition; interference; standing waves on strings; sound waves (introductory).

Optional Topics

• Thermodynamics (Introduction): Temperature scales; thermal expansion; heat and specific heat; phase changes; first law of thermodynamics; introduction to the kinetic theory of gases (often covered at the end of PHY2048 at some institutions, deferred to PHY2049 at others).
• Properties of Matter: Elasticity (Young's, shear, bulk moduli); stress and strain.
• Damped and Forced Oscillations: Damping; driven oscillations; resonance.
• Sound Waves and Acoustics: Speed of sound; intensity and decibel scale; Doppler effect; beats.
• Computational Methods: Numerical solution of equations of motion; data analysis with Python, MATLAB, or spreadsheets.
• Laboratory Experiments (when integrated): Motion sensors and computer-based instrumentation; force tables; collision investigations; rotational dynamics; pendulum experiments; standing waves.

Resources & Tools

• Standard Textbooks: Fundamentals of Physics by Halliday, Resnick, and Walker (Wiley — most widely adopted in Florida); Physics for Scientists and Engineers by Serway and Jewett (Cengage); University Physics by Young and Freedman (Pearson); Physics for Scientists and Engineers by Tipler and Mosca (Macmillan); OpenStax University Physics Volume 1 (free, openstax.org)
• Online Homework Platforms: WileyPLUS (Halliday); Cengage WebAssign (Serway); Pearson Mastering Physics (Young/Freedman); LON-CAPA (some institutions, including UF historically)
• Required Calculator: Texas Instruments TI-84 Plus, TI-84 Plus CE; some institutions allow TI-89 or TI-Nspire CX CAS but prohibit CAS calculators on exams.
• Computational Tools: Python with VPython for visualization (popular in modern physics curricula); MATLAB; Mathematica; spreadsheets for data analysis
• Free Online Resources: Khan Academy Physics; OpenStax University Physics (free textbook); MIT OCW 8.01 Physics I (ocw.mit.edu, including video lectures by Walter Lewin); 3Blue1Brown video explanations; The Physics Classroom (physicsclassroom.com); HyperPhysics (hyperphysics.phy-astr.gsu.edu)
• Florida-Specific Resources: UF Department of Physics PHY2048 syllabus archive (phys.ufl.edu); FSU Department of Physics; UCF Department of Physics; community of physics tutors at Florida public colleges
• Laboratory Resources (when integrated): Vernier and PASCO motion sensors and probes; Logger Pro / Capstone software; common physics lab equipment

Career Pathways

PHY2048 is a foundational course required across nearly all engineering, physics, and STEM pathways at Florida public universities:

• Engineering Pathways – Required for transfer to all Florida public engineering programs (UF, USF, UCF, FAU, FIU, FAMU-FSU College of Engineering, FGCU, Florida Polytechnic, UNF, ERAU); part of the engineering A.A. transfer pathway.
• Physics and Astronomy Majors – Required first-semester course in the calculus-based physics sequence; foundation for upper-division mechanics, electromagnetism, quantum mechanics, and modern physics.
• Computer Science (advanced tracks) – Required at all Florida public universities for the Computer Science B.S. and computer engineering programs; foundation for computer graphics, robotics, and game physics.
• Mathematics Majors – Required for many mathematics B.S. tracks; foundation for mathematical methods of physics and applied mathematics pathways.
• Pre-Medical and Pre-Dental – Required for medical and dental school admission; physics is one of the four sections of the MCAT (Chemical and Physical Foundations of Biological Systems).
• Florida Industry Application – Calculus-based physics underpins Florida's aerospace and defense (Kennedy Space Center, SpaceX, Lockheed Martin, L3Harris, Boeing, Northrop Grumman, Blue Origin), advanced manufacturing, semiconductor (growing in central Florida), biomedical engineering, and oceanographic research sectors.

Special Information

Gen-Ed Core Designation

PHY2048 is part of Florida's General Education Core Course Options in the Natural Sciences (Physical Sciences) discipline area, established by the Florida Department of Education and codified in Florida Statute 1007.25. All Florida public colleges and universities accept PHY2048 as fulfilling the Gen-Ed Natural Sciences core requirement. Students must earn a grade of C or better for the course to satisfy degree requirements.

Prerequisite and Co-Requisite

Students must have completed (or be concurrently enrolled in) MAC2311 (Calculus I) with a grade of C or better. MAC2312 (Calculus II) is typically a co-requisite. Calculus is required, not just co-requisite — line, area, and volume integrals using single integration are used heavily in PHY2048. Students lacking calculus preparation should consider PHY2053 (General Physics, Algebra-Based) instead.

Course Variants and Lab Component

PHY2048 is offered as PHY2048 (lecture-only, 3-4 credits) and PHY2048C (combined lecture and laboratory, 4-5 credits). The separate lab section PHY2048L (1 credit, sometimes called PHYL2048) is taken concurrently with PHY2048 to provide hands-on laboratory experience. Florida public universities and most engineering programs require both lecture and lab.

PHY2048 vs. PHY2053

Florida offers two introductory physics sequences: PHY2048/2049 (calculus-based, required for engineering/physics/computer science) and PHY2053/2054 (algebra-based, suitable for biology, pre-medicine, pre-pharmacy, and other life-science pathways). Engineering and physics majors must take PHY2048; algebra-based physics will not satisfy major requirements.

Workload and Time Expectations

PHY2048 is widely considered one of the more demanding STEM courses. Most institutions expect 9-12 hours of weekly out-of-class work for the lecture component, including 4-6 hours on online homework problems, 2-3 hours studying notes and examples, and 2-3 hours in tutoring or study groups. Lab adds 2-4 hours weekly. DFW rates are historically elevated; success requires consistent practice with problem-solving and conceptual understanding alongside calculation skills.

Foundation for Upper-Division Coursework

PHY2048 is the prerequisite for PHY2049 (General Physics with Calculus II), which covers electricity and magnetism, and indirectly for upper-division engineering and physics courses including dynamics, thermodynamics, fluid mechanics, electromagnetic theory, classical mechanics, and modern physics.